Rotor with flattened exit pressure profile

ABSTRACT

A rotor blade comprises an airfoil extending radially from a root section to a tip section and axially from a leading edge to a trailing edge, the leading and trailing edges defining a curvature therebetween. The curvature determines a relative exit angle at a relative span height between the root section and the tip section, based on an incident flow velocity at the leading edge of the airfoil and a rotational velocity at the relative span height. In operation of the rotor blade, the relative exit angle determines a substantially flat exit pressure ratio profile for relative span heights from 75% to 95%, wherein the exit pressure ratio profile is constant within a tolerance of 10% of a maximum value of the exit pressure ratio profile.

STATEMENT OF GOVERNMENT INTEREST

This invention was made with government support under contract numberNAS3-01138 awarded by NASA. The government has certain rights in theinvention.

BACKGROUND

This invention relates generally to turbomachinery, and specifically toturbine rotor components. In particular, the invention concerns a fan orcompressor rotor for a gas turbine engine.

Gas turbine engines (or combustion turbines) are built around a powercore made up of a compressor, combustor and turbine, arranged in flowseries with an upstream inlet and downstream exhaust. The compressorcompresses air from the inlet, which is mixed with fuel in the combustorand ignited to generate hot combustion gas. The turbine extracts energyfrom the expanding combustion gas, and drives the compressor via acommon shaft. Energy is delivered in the form of rotational energy inthe shaft, reactive thrust from the exhaust, or both.

Gas turbine engines provide efficient, reliable power for a wide rangeof applications, including aviation and industrial power generation.Small-scale engines including auxiliary power units typically utilize aone-spool design, with co-rotating compressor and turbine sections.Larger-scale jet engines and industrial gas turbines (IGTs) aregenerally arranged into a number of coaxially nested spools, whichoperate at different pressures and temperatures, and rotate at differentspeeds.

The individual compressor and turbine sections in each spool aresubdivided into a number of stages, which are formed of alternating rowsof rotor blade and stator vane airfoils. The airfoils are shaped toturn, accelerate and compress the working fluid flow, and to generatelift for conversion to rotational energy in the turbine.

Ground-based industrial gas turbines can be quite large, utilizingcomplex spooling systems for increased efficiency. Power is deliveredvia an output shaft connected to an electrical generator, or othermechanical load. Industrial turbines can also be configured forcombined-cycle operation, in which additional energy is extracted fromthe exhaust stream, for example using a low pressure steam turbine.

Aviation applications include turbojet, turbofan, turboprop andturboshaft engines. In turbojet engines, thrust is generated primarilyfrom the exhaust. Modern fixed-wing aircraft generally employ turbofanand turboprop designs, in which the low pressure spool is coupled to apropulsion fan or propeller. Turboshaft engines are typically used onrotary-wing aircraft, including helicopters.

Turbofan engines are commonly divided into high and low bypassconfigurations. High bypass turbofans generate thrust primarily from thefan, which drives airflow through a bypass duct oriented around theengine core. This design is common on commercial aircraft and militarytransports, where noise and fuel efficiency are primary concerns.

Low bypass turbofans generate proportionally more thrust from theexhaust flow, providing greater specific thrust for use on supersonicfighters and other high-performance aircraft. Unducted (open rotor)turbofans and ducted propeller configurations are also known, and thereare also counter-rotating and aft-mounted designs.

Turbofan engine performance depends on precise control of the workingfluid flow, including the pressure profile across each of the compressorand fan stages. Where engine noise and efficiency are factors, they posecompeting demands on fan and compressor blade design.

SUMMARY

This invention concerns a rotor blade, a rotor stage formed of aplurality of the rotor blades, and a turbine engine utilizing the rotorstage. The rotor blade has a leading edge, a trailing edge, a rootsection and a tip section, with an airfoil portion extending radiallyfrom the root section to the tip section, and axially from the leadingedge to the trailing edge.

The curvature of the airfoil is defined between the leading and trailingedges, and at a relative span height between the root section and thetip section. In operation of the rotor blade, the curvature determines arelative exit angle at the trailing edge, based on the incident flowvelocity at the leading edge and the rotational velocity of the blade atthe relative span height. The relative exit angle determines asubstantially constant exit pressure ratio profile for relative spanheights from 75% to 95%, within a tolerance of 10% of the maximum valueof the exit pressure ratio profile.

A rotor blade comprises a leading edge, a trailing edge, a root sectionand a tip section. An airfoil extends radially from the root section tothe tip section and axially from the leading edge to the trailing edge.The leading and trailing edges defining a curvature therebetween. Inoperation of the rotor blade, the curvature determines a relative exitangle at a span height between the root section and the tip section,based on an incident flow velocity at the leading edge of the airfoiland a rotational velocity at the relative span height. In operation ofthe rotor blade, the relative exit angle determines an exit pressureratio profile that is substantially constant for relative span heightsfrom 75% to 95%, within a tolerance of 10% of a maximum value of theexit pressure ratio profile.

In additional or alternative embodiments of any of the foregoingembodiments, the exit pressure ratio profile is non-decreasing forrelative span heights from 50% to 95%. In additional or alternativeembodiments of any of the foregoing embodiments, the tolerance is 2% ofthe maximum value of the exit pressure ratio profile. In additional oralternative embodiments of any of the foregoing embodiments, the exitpressure ratio profile has an absolute value of at least 1.3 for each ofthe relative span heights from 75% to 95%.

In additional or alternative embodiments of any of the foregoingembodiments, the relative exit angle is defined according to angle β₂ orangle β₂′ as set forth in Table 1 herein for relative span heights from75% to 95%, within a tolerance of two degrees (±2°). In additional oralternative embodiments of any of the foregoing embodiments, therelative exit angle is defined according to angle β₂ or angle β₂′ asprovided in Table 1 herein, for relative span heights from 5% to 95% andwithin a tolerance of one degree (±1°).

In additional or alternative embodiments of any of the foregoingembodiments, a gas turbine engine comprises the rotor blade. Inadditional or alternative embodiments of any of the foregoingembodiments, a rotor stage comprises a plurality of circumferentiallyarranged rotor blades, wherein in operation of the rotor stage the exitpressure ratio profile has an absolute value of at least 1.3 for each ofthe relative span heights from 75% to 95%.

In additional or alternative embodiments of any of the foregoingembodiments, a gas turbine engine comprises the rotor stage, wherein inoperation of the gas turbine engine the exit pressure ratio profile hasan absolute value of at least 1.4 for each of the relative span heightsfrom 75% to 95%. In additional or alternative embodiments of any of theforegoing embodiments, the exit pressure ratio profile has an absolutevalue of at least 1.4 for relative span heights between 95% and 98%.

A rotor comprises a rotor hub and a plurality of airfoils rotationallycoupled to the rotor hub, each airfoil extending axially from a leadingedge to a trailing edge and radially from a root section proximate therotor hub to a tip section opposite the rotor hub, the leading edge andthe trailing edge defining a curvature therebetween. In operation of therotor, the curvature determines a relative exit angle at a relative spanheight between the root section and the tip section, based on anincident flow velocity at the leading edge of the airfoil and arotational velocity of the airfoil at the relative span height. Inoperation of the rotor, the relative exit angle determines asubstantially uniform exit pressure ratio for span heights from 75% to95%, within a tolerance of 10% of a maximum of the exit pressure ratio.

In additional or alternative embodiments of any of the foregoingembodiments, the tolerance is 2% of the maximum of the exit pressureratio. In additional or alternative embodiments of any of the foregoingembodiments, the exit pressure ratio is non-decreasing for relative spanheights from 50% to 95%. In additional or alternative embodiments of anyof the foregoing embodiments, the relative exit angle is definedaccording to angle β₂ or angle β₂′ as provided in Table 1 herein forrelative span heights from 25% to 95%, within a tolerance of one degree(±1°).

In additional or alternative embodiments of any of the foregoingembodiments, a fan stage comprises the rotor, wherein the exit pressureratio has an absolute value of at least 1.3 for each of the relativespan heights from 75% to 95%. In additional or alternative embodimentsof any of the foregoing embodiments, a turbofan engine comprises the fanstage, wherein the exit pressure has an absolute value of at least 1.4for each of the relative span heights from 75% to 95%. In additional oralternative embodiments of any of the foregoing embodiments, the exitpressure ratio has an absolute value of at least 1.4 for relative spanheights between 95% and 98%.

A fan blade comprises an airfoil extending radially from a root sectionto a tip section, the airfoil having a leading edge and a trailing edgedefining a curvature at a relative span height between the root sectionand the tip section. In operation of the fan blade, the curvaturedetermines a relative exit angle at the trailing edge, based on anincident flow velocity at the leading edge and a rotational velocity ofthe airfoil at the relative span height. The relative air angle isdefined according to angle β₂ or angle β₂′ as provided in Table 1 hereinfor relative span heights between 75% and 95%, within a tolerance of twodegrees (±2°).

In additional or alternative embodiments of any of the foregoingembodiments, the relative air angle is defined according to angle β₂ orangle β₂′ as provided in Table 1 herein for relative span heightsbetween 25% and 95%, within a tolerance of one degree (±1°). Inadditional or alternative embodiments of any of the foregoingembodiments, in operation of the fan blade the relative air angledetermines a substantially flat exit pressure ratio profile for relativespan heights from 75% to 95%, wherein the exit pressure ratio profile issubstantially constant within a tolerance of 10% of a maximum value ofthe exit pressure ratio profile.

In additional or alternative embodiments of any of the foregoingembodiments, the tolerance is 2% of the maximum value of the exitpressure ratio profile. In additional or alternative embodiments of anyof the foregoing embodiments, the exit pressure ratio profile isnon-decreasing for relative span heights from 50% to 95%.

In additional or alternative embodiments of any of the foregoingembodiments a turbofan engine comprises the fan blade. In additional oralternative embodiments of any of the foregoing embodiments, a turbineengine comprise the fan blade, wherein in operation of the turbineengine the relative air angle determines an exit pressure ratio that hasan absolute value of at least 1.3 for each of the relative span heightsfrom 75% to 95%. In additional or alternative embodiments of any of theforegoing embodiments, the exit pressure ratio has an absolute value ofat least 1.4 at a relative span height of 97%.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view of a gas turbine engine having a fanrotor with a flattened exit pressure profile.

FIG. 2A is a perspective view of a rotor blade having a flattened exitpressure profile.

FIG. 2B is a cross sectional view of the rotor blade, illustratingleading edge and trailing edge velocity triangles.

FIG. 3A is a relative air angle profile for the rotor blade.

FIG. 3B is a relative air angle profile for the rotor blade, using analternate angular definition.

FIG. 4 is a stagnation pressure ratio profile for the rotor blade.

DETAILED DESCRIPTION

FIG. 1 is a cross-sectional view of gas turbine engine 10, in a turbofanconfiguration. In this configuration, gas turbine engine 10 includespropulsion fan 12 with fan exit guide vanes (FEGVs) 13 mounted insidebypass duct 14. The power core includes compressor section 16, combustor18 and turbine section 20.

Propulsion fan 12 has a flattened exit pressure profile to decrease wakeinteractions with fan exit guide vanes 13, reducing the noise profile ofgas turbine engine 10 and improving engine performance by bettermanaging downstream vorticity in bypass duct 14. The flattened exitpressure profile is defined in terms of the pressure ratio across fanrotor 12, using an aerodynamic blade geometry based on airfoil curvatureand relative exit (air) angle to define the stagnation pressure ratio ortotal pressure head across fan rotor 12, as described below.

In the two-spool, high bypass configuration of FIG. 1, compressorsection 16 includes low pressure compressor (LPC) 22 and high pressurecompressor (HPC) 24. Turbine section 20 comprises high pressure turbine(HPT) 26 and low pressure turbine (LPT) 28.

Low pressure compressor 22 is rotationally coupled to low pressureturbine 28 via low pressure (LP) shaft 30, forming the LP spool or lowspool. High pressure compressor 24 is rotationally coupled to highpressure turbine 26 via high pressure (HP) shaft 32, forming the HPspool or high spool.

In operation of gas turbine engine 10, fan 12 accelerates air flow frominlet 34 through bypass duct 14, generating thrust. The core airflow iscompressed in low pressure compressor 22 and high pressure compressor24, then mixed with fuel in combustor 18 and ignited to generatecombustion gas.

The combustion gas expands to drive high and low pressure turbines 26and 28, which are rotationally coupled to high pressure compressor 24and low pressure compressor 22, respectively. Expanded combustion gasesexit through exhaust nozzle 36, which is shaped to generate additionalthrust from the exhaust gas flow.

In advanced turbofan designs, low pressure shaft 30 is coupled to fan 12via geared drive mechanism 38, providing improved fan speed control forincreased efficiency and reduced engine noise. Propulsion fan 12 mayalso function as a first-stage compressor for gas turbine engine 10,with low pressure compressor 22 performing as an intermediate-stagecompressor or booster. Alternatively, the low pressure compressor stagesare absent, and air from fan 12 is provided directly to high pressurecompressor 24, or to an independently rotating intermediate compressorspool.

Gas turbine engine 10 thus encompasses a range of different shaft andspool geometries, including one-spool, two-spool and three-spoolconfigurations, in both co-rotating and counter-rotating designs. Gasturbine engine 10 may also be configured as a low bypass turbofan, anopen-rotor turbofan, a ducted or unducted propeller engine, or anindustrial gas turbine.

Fan and compressor noise contributions have both tonal and broadbandcomponents, each with significance for gas turbine engine design. Whenthe fan or compressor rotor is modified to flatten the exit pressureratio, wake interactions are decreased and the overall noise output isreduced. The size of the corresponding rotor stages can also reduced, ascompared to larger designs that would otherwise be required to lower thenoise signature. The flattened fan exit pressure ratio profile of gasturbine engine 10 may thus provide improved fuel efficiency with lessnoise, while reducing engine size and weight.

A substantial component of engine noise is generated by fan 12,particularly where the fan blade wakes interact with fan exit guidevanes 13. Noise during the takeoff and landing phases of flight has thusbecome a major driver in the design of gas turbine engines for aviation.In ultra high bypass ratio turbofans, for example, other jet noisesources may be substantially reduced, making fan noise appear morepronounced, as a relative contribution to the total noise output.

There are similar blade/vane interactions in compressor (or impeller)section 16, and aero-derivative turbine components and design techniquesare also used in other industries. Thus, the flattened fan pressureratio profiles described here have broad utility in both fan andcompressor rotor design for aviation and ground-based turbine engines,including, but not limited to, turbofan engines, turboprop engines andindustrial gas turbines.

FIG. 2A is a perspective view of rotor blade 40 for the fan orcompressor stage of a gas turbine engine. In this particularconfiguration, rotor blade 40 includes dovetail mount 42 and airfoilportion 44, with pressure surface 46 (front side) and suction surface 48(back side) extending axially from leading edge 50 to trailing edge 52.Airfoil sections S (dashed lines) are defined at relative span heightsH, where span heights H extend radially from hub or root section 54, at0% relative span, to airfoil tip section 56, at 100% relative span.

Rotor/vane interaction noise stems from turbulent wake flows generatedby upstream rotor stages, which induce unsteady pressure gradients whenthey impinge on downstream vanes. The wake-induced pressure patterns donot have to be circumferentially or radially non-uniform to radiatenoise, but the mean unsteady flow is circumferentially non-uniform,resulting in increased noise. To address this problem, airfoil sectionsS are designed with aerodynamic curvature to flatten the exit pressureratio profile of rotor blade 40, reducing noise contributions whilemaintaining rotor efficiency.

FIG. 2B is a cross-sectional view of rotor airfoil 44, illustratingvelocity triangles at leading and trailing edges 50 and 52,respectively. In operation, airfoil 44 has circumferential rotationalvelocity U, perpendicular to engine axis A, and as defined at aparticular span height H (see FIG. 2A).

Flow on leading edge 50 of airfoil 44 is incident at “absolute” velocityV₁, measured in the engine frame. Incident velocity V₁ may besubstantially axial, or include axial, radial and circumferentialcomponents. In flight applications, the axial component of incidentvelocity V₁ may include airspeed, for example where airspeed results inan axial flow component onto the fan or compressor section of a turbofanor turboprop engine.

Relative incident velocity W₁ is measured in the frame of airfoil 44(the rotor frame), making angle β₁ with respect to incident velocity V₁,as measured in the engine frame. Relative incident velocity W₁ hascomponent W_(θ1)=−U along the rotational (circumferential) direction.

Flow exits trailing edge 52 of airfoil 44 at relative exit velocity W₂,measured in the rotor fame. Relative exit velocity W₂ makes angle β₂with respect to axial component V_(X2) of exit velocity V₂, and hascircumferential component W_(θ2). “Absolute” exit velocity V₂ ismeasured in the engine frame, making angle α₂ with respect to axialcomponent V_(X2), with circumferential component V_(θ2) (or C_(θ2))along the direction of rotation.

Relative air angle (or relative exit angle) β₂ is defined in the rotorframe, between relative exit flow velocity W₂ and the axial direction attrailing edge 52 of airfoil 44. Alternatively, complementary relativeangle β₂′ is used, where β₂′=90°−β₂.

Any of angles α₁, β₁ and β₂ may also be defined using other conventions,either complementary or otherwise. In addition, any differences Δ inangle may be defined with either a positive or negative sense, dependingon the selected convention for angles α₁, β₁, and β₂.

FIG. 3A is a plot of relative angle β₂ for a rotor airfoil (or blade)with a flattened exit pressure profile (solid line), as compared to areference rotor airfoil (dashed line). The relative (exit) angle isgiven on the vertical axis (in degrees), as a function of relative spanheight along the horizontal (in percent).

FIG. 3B a plot of complementary air angle β₂′=90°−β₂, for a rotorairfoil with a flattened exit pressure profile (solid line), as comparedto a reference rotor airfoil (dashed line). The complementary (exit)angle is given on the vertical axis (in degrees), as a function ofrelative span height along the horizontal (in percent).

FIG. 4 is a plot of the downstream (exit) pressure profile (stagnationpressure ratio) for a rotor airfoil with a flattened pressure profile(solid line), as compared to a reference rotor blade (dashed line). Theexit pressure profile is given in terms of the pressure ratio across therotor blade (vertical axis, in normalized, dimensionless units), as afunction of relative span height (horizontal axis, in percent). Thecorresponding relative (exit) angles and pressure ratio (PR) values areprovided in Table 1.

The dashed line in FIG. 4 represents the reference airfoil of FIG. 3A or3B. The reference exit pressure ratio has a peak at approximately 75%span, dropping off substantially (by more than 10%) between 75% and 90%span, even more substantially (by more than 30%) toward 100% span (seeTable 1). As seen by the downstream vanes, these pressure patterns causea non-uniform velocity distribution along the corresponding span of thestator stage, resulting in an increased angle of attack, greaterturbulent losses, and more noise production.

The solid line in FIG. 4 shows that aerodynamic blade curvature candefine a relative exit angle profile with a flatter exit pressureprofile. In one particular design, the exit pressure ratio alsoincreases monotonically across the full span of the blade, including theouter 50-100% span, remaining substantially flat across 75-100% span,within a tolerance of ±0.010.

This results in a more uniform pressure and velocity profile across thespan of the blade, reducing downstream turbulent losses and noise.Alternatively, the pressure profile may decrease slightly at 90-100%span, for example by less than 5% or less than 10% (normalized), or byless than 0.10 or less than 0.15 in the scaled (absolute) pressure ratiovalues, in order to further improve performance.

The angular values in Table 1 have a nominal point-to-point tolerance ofa tenth of a degree (±0.1°), with an absolute tolerance ranging up toone degree (±1°) or two degrees (±2°), depending on application and thecorresponding tolerance in the selected pressure ratio. Alternatively,the angular tolerance is one-half degree (±0.5°)

Both normalized and absolute pressure ratio values are provided in Table1, with a nominal point-to-point tolerance of ±0.002. The absolutetolerance ranges from ±0.05, ±0.10, and ±0.15 to ±0.20 or more,depending on application and the corresponding tolerance in the selectedair angle.

The normalized pressure ratios in Table 1 can be scaled to aone-dimensional average of the values or based on a particular spanlocation, for example midspan. The absolute values are scaled to yieldparticular physical values of the actual pressure ratio, as measuredacross a rotating blade, for example using a scale factor ofS=1.35±0.05. Other scale factors S range from about S=0.8 to aboutS=1.6, for example S=0.8, S=0.9, S=1.0, S=1.1, S=1.2, S=1.3, S=1.4,S=1.5, or S=1.6.

Relative angles β₂ (or β₂′) of airfoil 44 are selected to achieve auniform downstream pressure pattern, with a flat exit pressure profileas compared to the reference blade. The exit pressure profile is definedby the physical blade geometry, and does not depend on the conventionused to measure the relative air (or exit) angles, or other angularconvention.

In particular, the flat exit pressure profile of FIG. 4 is determined bythe aerodynamic design of airfoil 44, as shown in FIGS. 2A and 2B. Theaerodynamic design of airfoil 44, in turn, is determined by thecurvature of camber lines C as defined along span height H, includingthe corresponding chord length, flow area and relative air angles β₂ (orβ₂′).

Thus, the geometry of airfoil 44 may be defined by the relative angleprofile, as given in Table 1 for various span heights between 0% and100%. Alternatively, the relative angle profile may be defined as adifference (Δ) with respect to a reference airfoil, or in terms ofcomplementary angle β₂′.

Table 1 and FIGS. 3A and 3B provide particular examples of relative exitangles that determine the flat pressure profile of FIG. 4, but otherrelative angle profiles may be used. The relative angles also varywithin the stated tolerances, and utilize different angular conventions.In addition, the pressure ratio profile depends upon blade height androtational velocity, as described below.

Conversely, the aerodynamic design of airfoil 44 may be determined bythe pressure ratio profiles of FIG. 4, and the corresponding PR valuesin Table 1. In particular, the pressure ratio determines the relativeexit angle profile (β₂ or β₂′) for a given span height and rotationalvelocity, based on the curvature of camber lines C. Note, however, thatpressure ratios PR also vary within the stated tolerances, and may bedescribed in either normalized or absolute (scaled) terms.

Thus, the geometry of airfoil 44 may be defined either in terms of therelative exit angle or the pressure ratio profile, as a function of therelative span height between 0% (root section) and 100% span (tipsection), for a given range of blade height and rotational speeds. Dueto endwall effects, however, the span range may be modified or limitedto regions of well defined pressure ratios PR. Alternatively, the spanrange is defined over particular portions of the for example the bladetip or midspan regions.

Thus, the lower end of the span range may be defined from substantially0% span, or as a range extending from or above about 1% span, about 2%span, or about 5% span. Similarly, the higher end of the span range maybe defined up to substantially 100% span, or as a range extending up toor below about 95% span, 98% span or 99% span.

The midspan range may be defined at approximately 50% span, or fromabout 25% to about 75% span. Other span ranges are also contemplated,including any combination of particular relative span values provided inTable 1, along with the corresponding pressure ratios and relativeangles β₂ and β₂′.

The flat pressure ratio profile design techniques described here areapplicable to blades operated at subsonic, transonic and supersonicspeeds. Representative blade outer diameters range from 50-100 inches(127-254 cm), or 25-50 inches (63-127 cm) in height measured from theengine axis at full span. For shorter blades, representative diametersrange from about 30-50 inches (76-127 cm), or 15-25 inches (38-64 cm) inheight from the engine axis. For longer blades, representative diametersrange up to 100-140 inches (254-356 cm), or 50-70 inches (127-175 cm) inheight from the engine axis. Representative rotational speeds range from2,000-6,000 RPM, extending down to 1,000-3,000 RPM for longer blades andup to 5,000-10,000 RPM for shorter blades.

While this invention has been described with reference to exemplaryembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the spirit and scope of theinvention. In addition, modifications may be made to adapt a particularsituation or material to the teachings of the invention, withoutdeparting from the essential scope thereof. Therefore, the invention isnot limited to the particular embodiments disclosed herein, but includesall embodiments falling within the scope of the appended claims.

TABLE 1 Pressure Ratio and Relative Angle Profiles Relative Angle Comp.Span Pressure Ratio β₂ ref. Δ β₂′ (%) Normal Scaled (deg) (deg) (deg)(90° − β₂) 0 0.886 1.192 −13.5 −15.2 1.7 103.5 1 0.887 1.194 −12.0 −13.71.7 102.0 2 0.888 1.196 −9.5 −11.1 1.6 99.5 3 0.889 1.198 −8.5 −10.0 1.598.5 4 0.891 1.200 −7.0 −8.3 1.3 97.0 5 0.892 1.202 −5.5 −6.6 1.1 95.5 60.894 1.204 −4.5 −5.4 0.9 94.5 7 0.896 1.207 −3.5 −4.2 0.7 93.5 8 0.8981.210 −2.0 −2.5 0.5 92.0 9 0.901 1.213 −1.0 −1.2 0.2 91.0 10 0.903 1.2170.0 0.0 0.0 90.0 11 0.906 1.220 1.0 1.3 −0.3 89.0 12 0.908 1.223 2.0 2.6−0.6 88.0 13 0.911 1.227 2.5 3.4 −0.9 87.5 14 0.913 1.230 3.5 4.7 −1.286.5 15 0.916 1.234 4.5 5.9 −1.4 85.5 16 0.918 1.237 5.0 6.5 −1.5 85.017 0.921 1.241 6.0 7.6 −1.6 84.0 18 0.924 1.245 7.0 8.5 −1.5 83.0 190.926 1.248 7.5 8.8 −1.3 82.5 20 0.929 1.252 8.0 9.1 −1.1 82.0 21 0.9321.255 8.5 9.4 −0.9 81.5 22 0.934 1.259 9.5 10.1 −0.6 80.5 23 0.937 1.26210.0 10.4 −0.4 80.0 24 0.940 1.266 11.0 11.2 −0.2 79.0 25 0.942 1.26911.5 11.5 0.0 78.5 26 0.945 1.273 12.0 11.9 0.1 78.0 27 0.947 1.277 12.512.3 0.2 77.5 28 0.950 1.280 13.0 12.7 0.3 77.0 29 0.952 1.283 13.5 13.10.4 76.5 30 0.954 1.286 14.0 13.4 0.6 76.0 31 0.957 1.289 14.5 13.8 0.775.5 32 0.959 1.292 15.0 14.2 0.8 75.0 33 0.961 1.295 15.5 14.5 1.0 74.534 0.964 1.298 16.0 14.9 1.1 74.0 35 0.966 1.301 16.5 15.2 1.3 73.5 360.968 1.304 17.5 16.1 1.4 72.5 37 0.970 1.307 18.0 16.5 1.5 72.0 380.972 1.310 18.5 16.8 1.7 71.5 39 0.974 1.313 19.0 17.2 1.8 71.0 400.976 1.315 19.5 17.6 1.9 70.5 41 0.978 1.317 20.0 18.0 2.0 70.0 420.980 1.320 20.5 18.4 2.1 69.5 43 0.982 1.323 21.0 18.9 2.1 69.0 440.984 1.326 21.5 19.3 2.2 68.5 45 0.986 1.328 22.0 19.7 2.3 68.0 460.988 1.331 22.5 20.2 2.3 67.5 47 0.990 1.334 23.0 20.7 2.3 67.0 480.991 1.336 23.5 21.1 2.4 66.5 49 0.993 1.338 24.0 21.6 2.4 66.0 500.995 1.340 24.5 22.1 2.4 65.5 51 0.997 1.342 25.0 22.6 2.4 65.0 520.999 1.345 25.5 23.2 2.3 64.5 53 1.001 1.347 26.0 23.7 2.3 64.0 541.002 1.350 26.5 24.3 2.2 63.5 55 1.004 1.352 27.0 24.8 2.2 63.0 561.006 1.355 27.5 25.4 2.1 62.5 57 1.008 1.357 28.0 26.0 2.0 62.0 581.009 1.359 28.0 26.1 1.9 62.0 59 1.011 1.362 28.5 26.6 1.9 61.5 601.013 1.364 29.0 27.2 1.8 61.0 61 1.014 1.366 29.5 27.8 1.7 60.5 621.016 1.368 30.0 28.3 1.7 60.0 63 1.017 1.370 30.5 28.9 1.6 59.5 641.019 1.372 31.0 29.4 1.6 59.0 65 1.020 1.374 31.5 30.0 1.5 58.5 661.021 1.376 32.0 30.5 1.5 58.0 67 1.023 1.378 32.0 30.6 1.4 58.0 681.024 1.380 32.5 31.2 1.3 57.5 69 1.025 1.382 33.0 31.7 1.3 57.0 701.026 1.383 33.5 32.3 1.2 56.5 71 1.028 1.385 33.5 32.4 1.1 56.5 721.029 1.385 34.0 33.0 1.0 56.0 73 1.030 1.386 34.5 33.6 0.9 55.5 741.031 1.387 34.5 33.7 0.8 55.5 75 1.032 1.389 35.0 34.2 0.8 55.0 761.033 1.390 35.5 34.8 0.7 54.5 77 1.034 1.391 36.0 35.4 0.6 54.0 781.035 1.392 36.0 35.5 0.5 54.0 79 1.036 1.393 36.5 36.1 0.4 53.5 801.036 1.394 37.0 36.7 0.3 53.0 81 1.036 1.395 37.5 37.4 0.1 52.5 821.037 1.396 37.5 37.5 0.0 52.5 83 1.037 1.396 38.0 38.1 −0.1 52.0 841.037 1.397 38.0 38.3 −0.3 52.0 85 1.037 1.397 38.5 38.9 −0.4 51.5 861.038 1.397 38.5 39.1 −0.6 51.5 87 1.038 1.398 39.0 39.8 −0.8 51.0 881.038 1.399 39.0 40.0 −1.0 51.0 89 1.038 1.399 39.5 40.7 −1.2 50.5 901.038 1.399 39.5 40.9 −1.4 50.5 91 1.038 1.399 39.5 41.1 −1.6 50.5 921.038 1.399 39.5 41.4 −1.9 50.5 93 1.038 1.399 40.0 42.1 −2.1 50.0 941.038 1.399 40.0 42.4 −2.4 50.0 95 1.038 1.400 40.0 42.7 −2.7 50.0 961.038 1.400 40.0 43.1 −3.1 50.0 97 1.038 1.400 40.0 43.4 −3.4 50.0 981.038 1.400 40.0 43.8 −3.8 50.0 99 1.038 1.400 39.5 43.7 −4.2 50.5 1001.038 1.400 39.5 44.2 −4.7 50.5

1. A rotor blade comprising: a leading edge, a trailing edge, a rootsection and a tip section; and an airfoil extending radially from theroot section to the tip section and axially from the leading edge to thetrailing edge, the leading and trailing edges defining a curvaturetherebetween; wherein, in operation of the rotor blade, the curvaturedetermines a relative exit angle at a span height between the rootsection and the tip section, based on an incident flow velocity at theleading edge of the airfoil and a rotational velocity at the relativespan height; and wherein, in operation of the rotor blade, the relativeexit angle determines an exit pressure ratio profile that issubstantially constant for relative span heights from 75% to 95%, withina tolerance of 10% of a maximum value of the exit pressure ratioprofile.
 2. The rotor blade of claim 1, wherein the exit pressure ratioprofile is non-decreasing for relative span heights from 50% to 95%. 3.The rotor blade of claim 1, wherein the tolerance is 2% of the maximumvalue of the exit pressure ratio profile.
 4. The rotor blade of claim 1,wherein the exit pressure ratio profile has an absolute value of atleast 1.3 for each of the relative span heights from 75% to 95%.
 5. Therotor blade of claim 1, wherein the relative exit angle is definedaccording to angle β₂ or angle β₂′ as set forth in Table 1 herein forrelative span heights from 75% to 95%, within a tolerance of two degrees(±2°).
 6. The rotor blade of claim 1, wherein the relative exit angle isdefined according to angle β₂ or angle β₂′ as provided in Table 1herein, for relative span heights from 5% to 95% and within a toleranceof one degree (±1°).
 7. A gas turbine engine comprising the rotor bladeof claim
 1. 8. A rotor stage comprising a plurality of circumferentiallyarranged rotor blades as set forth in claim 1, wherein in operation ofthe rotor stage the exit pressure ratio profile has an absolute value ofat least 1.3 for each of the relative span heights from 75% to 95%.
 9. Agas turbine engine comprising the rotor stage of claim 8, wherein inoperation of the gas turbine engine the exit pressure ratio profile hasan absolute value of at least 1.4 for each of the relative span heightsfrom 75% to 95%.
 10. The gas turbine engine of claim 9, wherein the exitpressure ratio profile has an absolute value of at least 1.4 forrelative span heights between 95% and 98%.
 11. A rotor comprising: arotor hub; and a plurality of airfoils rotationally coupled to the rotorhub, each airfoil extending axially from a leading edge to a trailingedge and radially from a root section proximate the rotor hub to a tipsection opposite the rotor hub, the leading edge and the trailing edgedefining a curvature therebetween; wherein, in operation of the rotor,the curvature determines a relative exit angle at a relative span heightbetween the root section and the tip section, based on an incident flowvelocity at the leading edge of the airfoil and a rotational velocity ofthe airfoil at the relative span height; and wherein, in operation ofthe rotor, the relative exit angle determines a substantially uniformexit pressure ratio for span heights from 75% to 95%, within a toleranceof 10% of a maximum of the exit pressure ratio.
 12. The rotor of claim11, wherein the tolerance is 2% of the maximum of the exit pressureratio.
 13. The rotor of claim 11, wherein the exit pressure ratio isnon-decreasing for relative span heights from 50% to 95%.
 14. The rotorblade of claim 11, wherein the relative exit angle is defined accordingto angle β₂ or angle β₂′ as provided in Table 1 herein for relative spanheights from 25% to 95%, within a tolerance of one degree (±1°).
 15. Afan stage comprising the rotor of claim 11, wherein the exit pressureratio has an absolute value of at least 1.3 for each of the relativespan heights from 75% to 95%.
 16. A turbofan engine comprising the fanstage of claim 15, wherein the exit pressure has an absolute value of atleast 1.4 for each of the relative span heights from 75% to 95%.
 17. Theturbofan engine of claim 16, wherein the exit pressure ratio has anabsolute value of at least 1.4 for relative span heights between 95% and98%.
 18. A fan blade comprising: an airfoil extending radially from aroot section to a tip section, the airfoil having a leading edge and atrailing edge defining a curvature at a relative span height between theroot section and the tip section; wherein, in operation of the fanblade, the curvature determines a relative exit angle at the trailingedge, based on an incident flow velocity at the leading edge and arotational velocity of the airfoil at the relative span height; whereinthe relative air angle is defined according to angle β₂ or angle β₂′ asprovided in Table 1 herein for relative span heights between 75% and95%, within a tolerance of two degrees (±2°).
 19. The fan blade of claim18, wherein the relative air angle is defined according to angle β₂ orangle β₂′ as provided in Table 1 herein for relative span heightsbetween 25% and 95%, within a tolerance of one degree (±1°).
 20. The fanblade of claim 18, wherein in operation of the fan blade the relativeair angle determines a substantially flat exit pressure ratio profilefor relative span heights from 75% to 95%, wherein the exit pressureratio profile is substantially constant within a tolerance of 10% of amaximum value of the exit pressure ratio profile.
 21. The fan blade ofclaim 20, wherein the tolerance is 2% of the maximum value of the exitpressure ratio profile.
 22. The fan blade of claim 20, wherein the exitpressure ratio profile is non-decreasing for relative span heights from50% to 95%.
 23. A turbofan engine comprising the fan blade of claim 18.24. A turbine engine comprising the fan blade of claim 18, wherein inoperation of the turbine engine the relative air angle determines anexit pressure ratio that has an absolute value of at least 1.3 for eachof the relative span heights from 75% to 95%.
 25. The turbine engine ofclaim 24, wherein the exit pressure ratio has an absolute value of atleast 1.4 at a relative span height of 97%.